Vertex Enumeration Package for
Convex Polytopes and Arrangements
Version 0.41 Beta
(Nevember 14, 1992)
by
Komei Fukuda and Ichiro Mizukoshi
This package contains Mathematica implementations of Avis-Fukuda
algorithms for enumerating all vertices of a convex polyhedron
given by a system of linear inequalities, and all vertices (points)
of an arrangement given similarly.
The package consists of the following six files
README.txt (This file itself)
VertexEnum.m (Mathematica package)
VE-Notebook.nb (Mathematica Notebook)
Power.m (Supplementary program
for VertexEnum.m)
FaceLattice.m (Supplementary package
to compute the face
lattice of a convex
polytope)
FL-Notebook.nb (Mathematica Notebook)
The notebooks explain how to use these packages through examples.
If your environment does not allow you to use notebooks, we suggest
you to get it printed before using the package. For the moment, the
notebook environment is supported by the Macintosh, NeXT, and Windows
versions of Mathematica.
This beta release is designed to run under Version 1.2/2.0/2.1 of
Mathematica.
Few bugs of Version 0.3 have been fixed, including its mishandling
of the case when the polyhedron is empty. Also, the notebook for
Version 0.3 has been slightly revised.
Please send your comments, bug reports etc. to:
Komei Fukuda or Ichiro Mizukoshi
Graduate School of Systems Management
University of Tsukuba, Tokyo
3-29-1 Otsuka, Bunkyo-ku
Tokyo 112, Japan
+81-3-3942-6876
fukuda@gssm.otsuka.tsukuba.ac.jp
or mizukosi@gssm.otsuka.tsukuba.ac.jp
Some remarks from Prof. Fukuda:
1. This package is rather old and slow, but it might be still useful for
small polytopes, say, of dimension less than or equal to 8.
2. VertexEnum.m does not detect unboundness.
For more information, please refer to
https://groups.google.com/forum/#!searchin/sci.math.symbolic/vertexenum/sci.math.symbolic/6ZI2QKOPvik/2lRn1QQEeN0J